Browsing by Author "Yuksel, Ugur"

Now showing 1 - 7 of 7

Citation Count: 3
Necessary and Sufficient Conditions for Associated Differential Operators in Quaternionic Analysis and Applications To Initial Value Problems
(Springer Basel Ag, 2013) Yuksel, Ugur; Yüksel, Uğur; Mathematics
This paper deals with the initial value problem of type in the space of generalized regular functions in the sense of Quaternionic Analysis satisfying the differential equation where is the time variable, x runs in a bounded and simply connected domain in is a real number, and is the Cauchy-Fueter operator. We prove necessary and sufficient conditions on the coefficients of the operator under which is associated with the operator , i.e. transforms the set of all solutions of the differential equation into solutions of the same equation for fixedly chosen t. This criterion makes it possible to construct operators for which the initial value problem is uniquely soluble for an arbitrary initial generalized regular function u (0) by the method of associated spaces constructed by W. Tutschke (Teubner Leipzig and Springer Verlag, 1989) and the solution is also generalized regular for each t.
Citation Count: 4
Necessary and Sufficient Conditions for First Order Differential Operators To Be Associated With a Disturbed Dirac Operator in Quaternionic Analysis
(Springer Basel Ag, 2015) Abbas, Usman Yakubu; Yüksel, Uğur; Yuksel, Ugur; Mathematics
Recently the initial value problem partial derivative(t)u = Lu :- Sigma(3)(i=1) A((i)) (t, x)partial derivative(xi) u + B(t, x)u + C(t, x) u(0, x) = u(0)(x) has been solved uniquely by N. Q. Hung (Adv. appl. Clifford alg., Vol. 22, Issue 4 (2012), pp. 1061-1068) using the method of associated spaces constructed by W. Tutschke (Teubner Leipzig and Springer Verlag, 1989) in the space of generalized regular functions in the sense of quaternionic analysis satisfying the equation D(alpha)u = 0, where D(alpha)u := Du + alpha u, alpha is an element of R, and D = Sigma(3)(j=1) e(j)partial derivative(xj) is the Dirac operator, x = (x(1), x(2), x(3)) is the space like variable running in a bounded domain in R-3 , and t is the time. The author has proven only sufficient conditions on the coefficients of the operator L under which L is associated with the operator D-alpha, i.e. L transforms the set of all solutions of the differential equation D(alpha)u = 0 into solutions of the same equation for fixedly chosen t. In the present paper we prove necessary and sufficient conditions for the underlined operators to be associated. This criterion makes it possible to construct all linear operators L for which the initial value problem with an arbitrary initial generalized regular function is always solvable.
Citation Count: 0
On a Dirichlet Problem for a Generalized Beltrami Equation
(Springer Basel Ag, 2018) Yüksel, Uğur; Yuksel, Ugur; Mathematics
In this article we study a Dirichlet problem for a hypercomplex Beltrami equation. We prove the existence of a unique solution of the problem and give a representation formula for the solution.
Citation Count: 8
On Common Fixed Point Theorems Without Commuting Conditions in Tvs-Cone Metric Spaces
(Eudoxus Press, Llc, 2011) Karapinar, Erdal; Karapınar, Erdal; Yuksel, Ugur; Yüksel, Uğur; Mathematics
In this manuscript, some common fixed point theorems without any commuting conditions investigated in TVS-valued metric spaces.
Citation Count: 2
A Schwarz Problem for the Generalized Beltrami Equation
(Taylor & Francis Ltd, 2011) Yuksel, Ugur; Yüksel, Uğur; Mathematics
This article deals with the Schwarz problem [image omitted] where is a regular domain of the complex plane. Sufficient conditions on the coefficients of the differential equation are obtained under which the operator of the corresponding problem for a system of integral equations is contractive in a certain Holder space. This leads to the existence of a unique solution of the original problem.
Citation Count: 9
Solution of Initial Value Problems With Monogenic Initial Functions in Banach Spaces With l_p<
(Birkhauser verlag Ag, 2010) Yuksel, Ugur; Yüksel, Uğur; Mathematics
This paper deals with the initial value problem of the type partial derivative u(t,x)/partial derivative t = Lu(t,x), u(0,x) = u(0)(x) (0.1) in Banach spaces with L-p-norm, where t is the time, u(0) is a monogenic function and the operator L is of the form Lu(t,x) := Sigma(A,B,i) C-B,i((A))(t,x)partial derivative u(B)(t,x)/partial derivative x(i)e(A). (0.2) The desired function u(t,x) = Sigma(B) u(B)(t,x)e(B) defined in [0, T] x Omega subset of R-0(+) x Rn+1 is a Clifford-algebra-valued function with real-valued components u(B)(t, x). We give sufficient conditions on the coefficients of the operator L under which L is associated to the Cauchy-Riemann operator D of CLIFFORD analysis. For such an operator L the initial value problem (0.1) is solvable for an arbitrary monogenic initial function u(0) and the solution is also monogenic for each t.
Citation Count: 50
Some Common Fixed Point Theorems in Partial Metric Spaces
(Hindawi Ltd, 2011) Yüksel, Uğur; Yuksel, Ugur; Karapınar, Erdal; Mathematics
Many problems in pure and applied mathematics reduce to a problem of common fixed point of some self-mapping operators which are defined on metric spaces. One of the generalizations of metric spaces is the partial metric space in which self-distance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. In this paper, some well-known results on common fixed point are investigated and generalized to the class of partial metric spaces.